Frequency Scanned Interferometer for ILC Tracker Alignment

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Frequency Scanned Interferometerfor ILC Tracker
Alignment

• Hai-Jun Yang, Sven Nyberg, Keith Riles
• University of Michigan, Ann Arbor
• 8th International Linear Collider Workshop
• SLAC, March 18-22, 2005

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ILC - Silicon Detector

• Barrel 5 layers, inner/outer radii 20/125
  cm,
• Silicon drift detector or microstrips
• ?r? 10 ?m, ?rz 20 ?m
• Forward 5 disks, double-sided silicon
  microstrips
• ?r? 7 ?m, ?rz 7 ?m
• Coverage - cos(?)0.99
• Boundary between barrel and
• forward disks - cos(?)0.80
• Wafer size 10cm x 10cm
• Wafer thickness 150 ?m

Ref SLAC-R-570 (2001) hep-ex/0106058
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A Possible SiD Tracker Alignment
752 point-to-point distance measurements
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Physics Goals and Background

• ? To Carry out RD toward a direct, quasi real
  time and remote way of
• measuring positions of critical tracker
  detector elements during operation.
• ? The 1-Dimension accuracy of absolute distance
  is on the order of 1 micron.
• Basic idea To measure hundreds of absolute
  point-to-point distances of tracker elements in 3
  dimensions by using an array of optical beams
  split from a central laser. Absolute distances
  are determined by scanning the laser frequency
  and counting interference fringes.
• Assumption Thermal drifts in tracker detector on
  time scales too short to collect adequate data
  samples to make precise alignment.
• Background some optical alignment systems
• RASNIK system used in L3, CHORUS and CDF,
• will be used in ATLAS
  and CMS
• Frequency Scanned Interferometer(FSI) will be
  used in ATLAS SCT A.F. Fox-Murphy et
  al., NIM A383, 229(1996)
• Focusing here on FSI system for ILC tracker
  detector

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Principle of Distance Measurement

• The measured distance can be expressed by
• constant end
  corrections
• c - speed of light, ?N No. of fringes, ?? -
  scanned frequency
• ng average refractive index of ambient
  atmosphere
• Assuming the error of refractive index is small,
  the measured precision is given by
• (?R / R)2 (??N / ?N)2 (??v / ??)2
• Example R 1.0 m, ?? 6.6 THz, ?N 2R??/c
  44000
• To obtain ?R ? 1.0 ?m, Requirements ??N
  0.02, ??v 3 MHz

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FSI Demonstration System (I)

• Tunable Laser New Focus Velocity 6308, 3-4 mW,
  665.1-675.2 nm.
• Retroreflector Edmund, D1, angle tolerance ?3
  arc seconds.
• Photodiode Thorlabs PDA55, DC-10MHz, Amplified
  Si Detector, 5 Gain Settings.
• Thorlabs Fabry-Perot Interferometer SA200, high
  finesse(gt200) to determine the relative
  frequency precisely, Free Spectral Range (FSR) is
  1.5 GHz, with peak FWHM of 7.5 MHz.
• Thermistors and hygrometer are used to monitor
  temperature and humidity respectively.
• PCI Card NI-PCI-6110, 5 MS/s/ch, 12-bit
  simultaneous sampling DAQ.
• PCI-GPIB Card NI-488.2, served as remote
  controller of laser.
• Computers 1 for DAQ and laser control, 3 for
  analysis.

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FSI Demonstration System (I)
Fabry-Perot Interferometer
Mirror
Photodetector
Beamsplitters
Retroreflector
Laser
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Temperature Measurements
Outside of Box
Inside of Box
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FSI with Optical Fibers (II)
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FSI with Optical Fibers (II)
? A key issue for the optical fiber FSI is that
the intensity of the return beams received by the
optical fiber is very weak. e.g. the core of the
single mode optical fiber has diameter of 5
?m. Geometrical Efficiency 6.25?1010
for a distance of 0.5 m ? A novelty in our
design is the use of a gradient index lens (GRIN
lens 0.25 pitch lens with D1mm, L2.58mm) to
collimate the output beam from the optical fiber.
The density of the outgoing beam is increased by
a factor of 1000 by using the GRIN lens. This
makes it possible to split the laser beam into
many beams to serve a set of interferometers
simultaneously.
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Multiple-Measurement Techniques

• If drift error(?) occurs during the laser
  scanning, it will be magnified by a factor of
  ?(? ? ?/?? 67 for full scan of our tunable
  laser),
• OPDmeasured OPDtrue ??
• ? Plastic box and PVC pipes are constructed to
  reduce thermal drift.
• Assuming a vibration with one frequency
• xvib(t) avib ?cos(2?fvibt ?vib)
• Fringe phase at time t
• ?(t) 2? ? OPDtrue 2xvib(t)/?(t)
• ?N ?(t)??(t0)/2? OPDtrue ???/c
  2xvib(t)/?(t)- 2xvib(t0)/?(t0)
• If we assume ?(t) ?(t0) ?, measured OPD can
  be written as,
• OPDmeas OPDtrue ? ? 2xvib(t)- 2xvib(t0)
  (1)
• OPDmeas OPDtrue ? ? ?
  4avibsin?fvib(t-t0) ? sin?fvib(tt0)?vib (2)
• ? Two new multiple-distance measurement
  techniques are presented to extract vibration and
  to improve the distance measurement precision
  based on Eq.1 and Eq.2, respectively.

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Two Multiple-Measurement Techniques
?Fix the measurement window size (t-t0) and shift
the window one F-P peak forward each time to
make a set of distance measurements. The average
value of all measurements is taken to be the
final measured distance of the scan.
?Fringes
?F-P Peaks FSR1.5 GHz
?If t0 is fixed, the measurement window size is
enlarged one F-P peak for each shift. An
oscillation of a set of measured OPD reflects the
amplitude and frequency of vibration.
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Vibration Measurement
? A PZT transducer was employed to produce
controlled vibration of the retroreflector,
fvib 1.01 ? 0.01 Hz, ampvib 0.14 ? 0.02 ?m

• ? Magnification factor ? for each distance
  measurement depends on the scanned frequency of
  the laser beam in the measurement window with
  smaller ? for larger window - plot(a). Since the
  vibration is magnified by ? for FSI during the
  scan, the expected reconstructed vibration
  amplitude is 10.0 ?m assuming ? 70 plot(b).
• ?The extracted vibration plot(c)
• fvib 1.007 ? 0.0001 Hz,
• ampvib 0.138 ? 0.0003 ?m

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Vibration Measurement

• Controlled vibration source with very low
  amplitude
• fvib 1.01 ? 0.01 Hz, ampvib 9.5 ? 1.5
  nanometers
• Measured vibration
• fvib 1.025 ? 0.002 Hz,
• ampvib 9.3 ? 0.3 nanometers
• ?Measurable range
• fvib 0.1 100 Hz,
• ampvib few nm 0.4 ?m

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Absolute Distance Measurements

• The scanning rate was 0.5 nm/s and the sampling
  rate was 125 KS/s.
• The measurement residual versus the No. of
  measurements/scan shown in Fig.,
• (a) for one typical scan,
• (b) for 10 sequential scans.
• ?It can be seen that the distance errors decrease
  with increasing Nmeas.
• Nmeas1, precision1.1 ?m (RMS)
• Nmeas1200, precision41 nm (RMS)
• ?Multiple-distance measurement technique is well
  suited for reducing vibration effects and
  uncertainties from fringe frequency
  determination, BUT not good for drift errors such
  as thermal drift.

(a)
(b)
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Absolute Distance Measurements
Each precision listed is for standard deviation
(RMS) of 10 scans.
Distance measurement precisions for various
setups using the multiple-distance-measurement
technique.
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Dispersion Effect

• Dispersive elements, beamsplitter, corner cube
  prism etc. can create significant offset in
  measured distance for FSI system since the small
  OPD change caused by dispersion is magnified by a
  factor of ?.
• Sellmeier formula for dispersion in crown glass
  (BK7)
• n2(?2)1B1?2 /(?2 -C1)B2?2 /(?2 -C2)B3?2
  /(?2 -C3)
• B11.03961212, B20.231792344, B31.01046945
• C10.00600069867, C20.0200179144, C3103.560653
• Numerical simulation results (thickness of the
  corner cube prism 1.86 cm)
• R_1 R_true 373.876 um, R_2000 R_true
  367.707 um
• R_1 R_2000 6.2 /- 0.2 um
• Real data - fitted result
• R_1 R_2000 6.14 /- 0.1 um
• ? Dispersion effects can be avoided by
• using hollow retroreflector and put
• the beamsplitters anti-reflecting
• surface facing the optical fiber.

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Error Estimations

• Error from uncertainties of fringe and frequency
  determination, dR/R 1.9 ppm if Nmeas 1200,
  dR/R 77 ppb
• Error from vibration. dR/R 0.4 ppm if Nmeas
  1200, dR/R 10 ppb
• Error from thermal drift. Temperature
  fluctuations are well controlled down to 0.5
  mK(RMS) in Lab by plastic box on optical table
  and PVC pipes shielding the volume of air near
  the laser beam. An air temperature change of 1 0C
  will result in a 0.9 ppm change of refractive
  index at room temperature. The drift will be
  magnified during scanning. if Nmeas 1200, dR/R
  0.9 ppm/K ? 0.5mK ? ?(94) 42 ppb.
• Error from air humidity and pressure, dR/R 10
  ppb.
• The total error from the above sources
  is 89 ppb which agrees well with the measured
  residual spread of 90 ppb
• over different days and times of
  measurement.

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Systematic Error Estimations

• The major systematic bias comes from
  uncertainty of the Free Spectral Range (FSR) of
  the Fabry Perot interferometer used to determine
  scanned frequency range precisely, the relative
  error would be dR/R 50 ppb if the FSR was
  calibrated by an wavemeter with a precision of 50
  ppb. A wavemeter of this precision was not
  available for the measurement described here.
• The systematic bias from the multiple-distance-m
  easurement technique was also estimated by
  changing the starting point of the measurement
  window, the window size and the number of
  measurements, the uncertainties typically range
  from 10-30 nanometers (lt 50 ppb).
• The systematic bias from uncertainties of
  temperature, air humidity and barometric pressure
  scales should have negligible effect.
• The total systematic error is 70 ppb.

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Comparison of FSI performances
? National Institute of Standards and Technology
(NIST) Air transport FSI, Distance 30 cm 5
m, Precision 250 nm by averaging measurements
of 80 independent scans. J.A. Stone et.al,
Applied Optics, V38. No. 28, 5981(1999)
? University of Oxford ATLAS Group Optical
fiber FSI, Distance 20 cm 1.2 m, Precision
215 nm by using dual-laser technique to reduce
drift errors P.A. Coe, Doctoral Thesis, U. of
Oxford, 2001
? University of Michigan ILC Group Optical
fiber FSI, Distance 10 cm 0.6 m (measurable
distance limited by bandwidth of our femtowatt
photodetector, 30-750 Hz) Precision 50 nm by
using new multiple-distance measurement
technique under well controlled laboratory
conditions. Vibration 0.1-100 Hz, gt few
nanometers, can be extracted precisely
using new vibration extraction
technique. physics/0409110, Accepted for
publication by Applied Optics, 2004
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Dual-Laser FSI (III)

• A dual-laser FSI intended to reduce the drift
  errors is under study currently. Two lasers are
  operating simultaneously, but the laser beams are
  isolated by using two choppers.

Laser 1 D1 Dtrue ?1?1 Laser 2 D2 Dtrue
?2?2 Drift errors ?1 ? ?2 ? Dtrue (D2 -
?D1) / (1 - ?), Where ? ?2 / ?1
Two Lasers
Two Choppers
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Fringes F-P Peaks for Dual-Laser FSI
Laser-1
Laser-2
Chopper edge effects and low photodiode duty
cycle per laser complicate measurement requires
study
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Summary and Outlook

• ? Two FSI demonstration systems, with or without
  optical fibers, were constructed to make
  high-precision absolute distance measurements.
• ? Two new multi-distance-measurement analysis
  techniques were presented to improve absolute
  distance measurement and to extract the amplitude
  and frequency of vibration.
• ? A high precision of 50 nm for distances up to
  60 cm under laboratory conditions was achieved.
• ? Major error sources were estimated, and the
  expected error was in good agreement with spread
  in data.
• ? We are investigating dual-laser scanning
  technique used by Oxford ATLAS group currently.
• ? Michigan group has extended the frontier of FSI
  technology, but much work lies ahead.

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BACKUP SLIDES
BACKUP SLIDE
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RASNIK Demonstration System
RASNIK provides alignment monitoring with
submicron precision, developed at NIKHEF.